# Power series

1. May 2, 2005

the function $$f(x) = \frac{10}{1+100*x^2}$$
is represented as a power series
$$f(x) = \sum_{n=0}^{\infty} C_nX^n$$

Find the first few coefficients in the power series:
C_0 = ____
C_1 = ____
C_2 = ____
C_3 = ____
C_4 = ____

well $$f(x) = \frac{10}{1+100*x^2}$$ can be written as $$10\sum_{n=0}^{\infty} (-100x^2)^n$$

for C_0, i got 10 because if you plug in n = 0, you get 10 (which is correct).
for c_1, when i plug in n=1, i get -1000, which is incorrect.
i tried doing the same for c_2-c_4, but it keeps telling me i get the wrong answer. does anyone know why?

2. May 2, 2005

### whozum

Im pretty sure you modeled the function incorrectly.

3. May 2, 2005

### Galileo

Write out a few terms of your expansion. What are the coefficients of the even powers of x in your expansion?

4. May 2, 2005

### Data

and more importantly, what are the coefficients of the odd powers of x?

5. May 3, 2005

i dont think i modeled it incorrectly, because there's a similar problem in the book, but maybe i made a mistake so who knows, but here are the first few terms....

10 - 1000x^2 + 10000x^4 -10000000x^6 + 1000000000x^8...

coefficients of the odd powers are zero....

but i cant seem to get the even coefficients correctly.... what am i doing wrong?

6. May 3, 2005

### Data

Looks fine to me except that your coefficient for $x^4$ is one power of ten too small. Remember that this expansion is only valid for $|x|<1/10$ too.